[N,k,chi] = [2,48,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Newform invariants
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
sage: f.q_expansion() # note that sage often uses an isomorphic number field
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you can click on its label.
Refresh table
\( p \)
Sign
\(2\)
\(-1\)
This newform does not admit any (nontrivial ) inner twists .
This newform subspace can be constructed as the kernel of the linear operator
\( T_{3} + 196634580372 \)
T3 + 196634580372
acting on \(S_{48}^{\mathrm{new}}(\Gamma_0(2))\).
$p$
$F_p(T)$
$2$
\( T - 8388608 \)
T - 8388608
$3$
\( T + 196634580372 \)
T + 196634580372
$5$
\( T - 20\!\cdots\!50 \)
T - 20669962168980750
$7$
\( T + 51\!\cdots\!96 \)
T + 51172881836896522696
$11$
\( T - 52\!\cdots\!52 \)
T - 5297430319653102012090852
$13$
\( T + 12\!\cdots\!02 \)
T + 125094137018739417081409402
$17$
\( T + 44\!\cdots\!26 \)
T + 44830025442540925573659584526
$19$
\( T + 11\!\cdots\!00 \)
T + 1111319860561156308410383992100
$23$
\( T + 17\!\cdots\!72 \)
T + 178238089260084834809121532218072
$29$
\( T + 30\!\cdots\!90 \)
T + 30534112362977188191390732250983690
$31$
\( T + 11\!\cdots\!28 \)
T + 110801717324244256756593954244061728
$37$
\( T - 62\!\cdots\!54 \)
T - 6203767833063528570721355158143068654
$41$
\( T + 35\!\cdots\!78 \)
T + 35669771283594680742424472586368472678
$43$
\( T - 33\!\cdots\!68 \)
T - 338085414102589873498086573597898665668
$47$
\( T + 22\!\cdots\!36 \)
T + 2298386467820046045287393257826261887536
$53$
\( T + 29\!\cdots\!02 \)
T + 29595651085041661560230876234553121751202
$59$
\( T - 40\!\cdots\!20 \)
T - 402897770467707194917911296294114858644020
$61$
\( T - 57\!\cdots\!42 \)
T - 575153391792220796561057524320411384118742
$67$
\( T + 18\!\cdots\!36 \)
T + 1868033100301939556103984556344225386618836
$71$
\( T - 55\!\cdots\!12 \)
T - 55201984112681452831941304628692429011115512
$73$
\( T + 79\!\cdots\!02 \)
T + 79182696974319051005003915162106408285767302
$79$
\( T - 88\!\cdots\!40 \)
T - 88275129763458787700378919632160122138091440
$83$
\( T + 73\!\cdots\!92 \)
T + 737730557224622917773365649736040155174606692
$89$
\( T + 82\!\cdots\!90 \)
T + 8277033948537162260782072894676071243017411990
$97$
\( T + 61\!\cdots\!46 \)
T + 61954178934472753824888537150641827226577342046
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